Let be three points in
.
Find |2b - a + 3c|.
We are asked to find ( |2\mathbf{b} - \mathbf{a} + 3\mathbf{c}| ) for [ \mathbf{a} = (1, 2, 3), \quad \mathbf{b} = (-5, 3, -2), \quad \mathbf{c} = (2, -4, 1). ] Step 1: _______ __________ ______ _____ __________ ________ ___.
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tate Green’s theorem, and apply it to evaluate
Where C is the ellipse .
Check if the following integrals are independent of path and evaluate those which are independent.
State whether the following statements are true or false. Give reasons for your answers.
(i)
(ii) A real-valued function of three variables which is continuous everywhere is differentiable.
(iii) The function , defined by
, is locally invertible at any
.
(iv) , defined by
is integrable.
(v) The function , defined by
, has an extremum at (0, 0).
Suppose S and C are subsets of . S is the unit open sphere with centre at the origin and C is the open cube
.
Which of the following is true. Justify your answer.
(i)
(ii)
(c) Identify the level curves of the following functions:
(i)
(ii)
Check the continuity and differentiability of the function at (0,0) where
Find the mass of the solid bounded by and
, the density function being
.
मान लीजिए कि S और C के उपसमुच्चय हैं। S मूल–बिन्दु पर केन्द्र वाला एकक विवृत गोलक है तथा C विवृत घन
।
निम्नलिखित में से कौनसा कथन सत्य है? अपने उत्तर की पुष्टि कीजिए।
(i)
(ii)
(ग) निम्नलिखित फलनों के स्तर वक्र ज्ञात कीजिए :
(i)
(ii)